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Miller chapter 3

I would think it is
mean = 0.7*0 + 0.3*1 = 0.3
variance = 0.7*(0-0.3)^2 + 0.3*(1-0.3)^2 = 0.063 + 0.147 = 0.21
std deviation = sqrt (0.21) = 0.458


New Member
Also need help with this question as well what is empirical probability if we roll a dice once what is the probability of receiving 3 on a dice (ans 18%)? in normal probability it is 1/6 right?


New Member
Hi ,

Kindly confirm why empirical probability for resultant 3 on a dice = 18 percent however the normal probability is 1/6 what is the formula for empirical probability?


Active Member
Do you mean die or dice? Empirical by definition is experimental, i.e. what is observed in the real world. The probability of rolling a 3 on a six sided die would be 1/6 assuming it’s a fair die, but you can experimentally roll it 100 times and see 3, 18 times, giving you an empirical probability of 18%. If it is indeed a fair die, as the sample increases we get closer to the true, 1/6 probability.

Without further context I cannot comment on the 18% probability further. Is this from a textbook or some article? Where did you get that number?


New Member

Will it be already given that if we roll 100 times we should get 18 and how did you conclude that?
Number of times getting 3
P(E) = (Total number of trials
/Total number of trials ) =(18/100)= 0.18 or 18 percent


David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi @praveenraj That's just an example; ie, a single simulation. If we roll a fair die 100 times, we expect 1/6*100 = 16.17, that is we expect about 16 or 17 of each. As a random variable, the fair die has an parametric (aka, analytical, theoretical) distribution that characterizes the population: it is uniform discrete where Pr(X = x) = 1/6. But every simulation of 100 throws produces a sample with non-uniform outcomes. My exhibit above shows one outcome; if we throw another 100, we will get a (slightly) different outcome, but probably not too dramatically different. Most of our realistic work is observing samples and fitting analytical distributions to them; e.g., we observe daily returns and, if they are approximately normal, we fit a (parametric) normal distribution to the observed sample. Thanks,